For TDP/PDP, as in Claim REF , the problem becomes trivial when \(n_\mathcal {B}\ge \min \lbrace n_\mathcal {I},n_\mathcal {O}\rbrace \) . Note that a variant of PDP, in which the required relations in the solution are functions can be viewed as an instance of the problem of Boolean functional synthesis, e.g. [1]}, [2]}.
